Prior to the current invention, most construction elements of any similar nature could be placed into one or more of four categories:                1) Stacking Blocks—which provide no means for self-retention of assembled structures, other than gravity; but require some form of bonding material if they are to be secured in their relative positions;        2) Member Suspended Interconnected Elements—which require rods or other secondary connective devices to determine and/or secure their relative positions in space;        3) Slotted Circular or Polygonal Discs—while interfitting or intercleaving, their teachings do not lend themselves to producing the non-planar elements required to emulate real world, molecular building blocks. Assemblies produced with such planar elements are not substantially space filled; and        4) Interfitting Surface Indentations—where complimentary patterns of protrusions and indentations provide for the alignment and mating of the surfaces of the generally polyhedral forms in a manner/direction which is orthogonal with respect to those mating surfaces.        
No prior art has attempted to produce self-interfitting, self-retaining construction elements which produce substantially space-filled structures/assemblies. Most construction elements of prior design attempt to make their use more obvious and easy; while a significant portion of the current invention's value as an entertainment device and educational tool is the mystery, puzzlement, and challenges it presents due to the tendency of its various embodiments to retain the natural restraints associated with real-world elemental building blocks. Some examples of these natural restraints demonstrated by the elements of the current invention are as follows:                1) the restricted intercleaving nature of the elements may be used to demonstrate the intercleaving nature of covalent chemical bonds;        2) some of the required assembly and disassembly methods for the elements are analogous to thermal contraction and expansion in solids;        3) other assembly and disassemble methods emulate crystal growing and cleaving;        4) the natural inclination for the elements to produce mirror image (enatiomorphic) structures may be used to demonstrate and better understand both right-handed rotating (dextrorotary) and left-handed (levorotary) formations, such as during growth of organic substances or crystals;        5) the self-similar nature of assembled supersets of the elements of the invention may be used to emulate the development of polymer compounds from smaller polymer and monomer building blocks;        6) the self-similar nature of the assembled elements may also be used in creating complex embodiments and assemblies, enabling a new means of representing the fractal nature of the physical world; and        7) the ability of select embodiments of the invention to more naturally implement assemblies with five-fold symmetry may assist in demonstrating recently discovered chemical compounds with similar symmetries.        
Accordingly, the building blocks (construction elements) of the invention are capable of not only modeling the net results of of molecular and crystal formation, but also of simulating the nature of the difficulties and processes involved in forming such chemical assemblages. Part of the challenge associated with the use of the current invention is that once one has determined which elements are needed and where each element must be placed, the user must still determine how to get them there; once again simulating the challenging nature of creating assemblies of chemical elements.
In summary, although many prior teachings demonstrate the combining of polyhedral elements into larger assemblies, each of them require some form of adhesive or secondary connection device or mechanism to implement the connection or to retain their interconnected alignments. Although most of the manufactures defined by the current invention do not result in fully space filled assemblages, all assemblies resulting from the use of the present invention are substantially more space-filling than any of the planar intercleaving manufactures of any prior art. No prior art provides generally polyhedral construction elements which non-perpendicularly mate, with respect to engaging surfaces, via interpenetrating vertices and/or edges. Finally no prior art provides the ability to produce the uniquely elegant assemblies enabled by the current invention.